Apply transformations with rotation and/or reflection. More...

#include <Transformation.hh>

Classes
struct	Properties
	Calculated properties about the transformation. More...

Type aliases
using	StorageSpan = Span< real_type const, 12 >
	Transformation type identifier.

using	Mat3 = SquareMatrixReal3
	Transformation type identifier.

static constexpr TransformType	transform_type ()
	Transformation type identifier.

static Transformation	from_inverse (Mat3 const &rot, Real3 const &trans)
	Construct by inverting another transformation.

	Transformation (Mat3 const &rot, Real3 const &trans)
	Construct with rotation and translation.

	Transformation ()
	Construct as an identity transform.

	Transformation (Translation const &)
	Promote from a translation.

	Transformation (SignedPermutation const &)
	Transformation type identifier.

	Transformation (StorageSpan)
	Construct inline from storage.

Mat3 const &	rotation () const
	Rotation matrix.

Real3 const &	translation () const
	Translation vector.

StorageSpan	data () const
	Get a view to the data for type-deleted storage.

Real3	transform_up (Real3 const &pos) const
	Transform from daughter to parent.

Real3	transform_down (Real3 const &parent_pos) const
	Transform from parent to daughter.

Real3	rotate_up (Real3 const &dir) const
	Rotate from daughter to parent.

Real3	rotate_down (Real3 const &parent_dir) const
	Rotate from parent to daughter.

Transformation	calc_inverse () const
	Calculate the inverse during preprocessing.

Properties	calc_properties () const
	Calculate properties about the matrix.

Detailed Description

Apply transformations with rotation and/or reflection.

Note: The nomenclature in this class assumes the translation vector and rotation matrix given represent "daughter-to-parent"! This is because we think of rotations being with respect to the daughter's origin rather than the parent's.

This class enables transforms between daughter and parent coordinate system. The transfer from a daughter into a parent system ("up" in a hierarchy of universes) is

\[ \mathbf{r}_p = \mathbf{R}\mathbf{r}_d + \mathbf{t}\:, \]

Where the subscripts p,d refer to the parent and daughter coordinate systems, respectively. The vector t is a translation vector. To go from the parent into the daughter system ("down" in a universe hierarchy) we apply the inverse:

\[ \mathbf{r}_d = \mathbf{R}^T(\mathbf{r}_p - \mathbf{t})\:. \]

where the transpose of R is equal to its inverse because the matrix is unitary.

The rotation matrix is indexed with C ordering, [i][j]. If a rotation matrix, it should be a orthonormal with a determinant is 1 if not reflecting (proper) or -1 if reflecting (improper). A transformation that applies a scaling has non-unit eigenvalues.

It is the caller's job to ensure a user-provided low-precision rotation matrix is orthonormal: see celeritas::orthonormalize . (Add CELER_VALIDATE to the calling code if constructing a transformation matrix from user input or a suspect source.)

Todo:: Scaling is not yet implemented correctly.

Member Function Documentation

◆ transform_down()

Real3 celeritas::Transformation::transform_down ( Real3 const & pos ) const

inline

Transform from parent to daughter.

Subtract the translation, then apply the inverse of the rotation matrix (its transpose).

◆ transform_up()

Real3 celeritas::Transformation::transform_up ( Real3 const & pos ) const

inline

Transform from daughter to parent.

Apply the rotation matrix, add the translation.

The documentation for this class was generated from the following files:

Classes

Type aliases

Detailed Description

Member Function Documentation

◆ transform_down()

◆ transform_up()